عدم تطابق نرخ ارز و سیاست پولی: جریان دو تعادل

We develop a model of a small economy whose residents choose whether to borrow in domestic or foreign currency. The central bank, in turn, chooses fixed or flexible exchange rates, taking the currency denomination of debts as given. We characterize the simultaneous determination of portfolios and exchange rate regime. Both floating and fixed rates can occur as equilibrium outcomes. “Fear of floating” may emerge endogenously and in association with a currency mismatch in assets and liabilities. If equilibria with both fixed rates and floating rates coexist, the latter is Pareto superior. Lessons for current “de-dollarization” proposals are discussed.

Emerging market countries have trouble letting their exchange rates float, and many countries that claim to float do not deliver on that promise. That is the conclusion of much recent empirical work, starting with Stein et al. (1999) and Calvo and Reinhart (2002).2 The reason, these papers argue, is a lethal mix of dollarization of liabilities and balance sheet effects: if corporate debts are denominated in dollars while the value of corporate assets depends on local currency (or if corporate revenues increase with the relative price of goods produced at home), sharp and unexpected currency movements matter for financial stability. The policy conclusion is that flexible exchange rates can be destabilizing, and therefore emerging market nations would be well advised to adopt alternative monetary arrangements, including currency boards and official dollarization. Such a view has become extremely influential, but even its most ardent advocates understand that it is only half the story. The claim is that floating is not feasible given that debts are dollarized. But, presumably, borrowers choose the amounts of debt to issue as peso and dollar-denominated bonds taking into account the risk–return characteristics of these securities. Recognizing that variances and covariances (especially with consumption) should then matter, Ize and Levy-Yeyati (2003), Ize and Parrado (2002), and Morón and Castro (2003) have extended standard portfolio theory to model endogenous dollarization in emerging markets. Their approach, however, takes as given the structure of shocks and, more importantly for our discussion, monetary and exchange rate policies. Since–as the recent debate has emphasized–exchange rate policies depend on portfolio choices but at the same time portfolio choices depend on anticipated exchange rate policies, the next question is inevitable: what are the implications of this interaction, if portfolios and exchange rate policy are both endogenous? In particular, what are the resulting policy outcomes? Is there a single outcome, or several ones? These are the issues on which this paper focuses. We build an extremely simple model of a small open economy in which domestic residents borrow internationally by issuing bonds denominated in both home and foreign currency. The currency composition of the debt plays a nontrivial role because markets are incomplete: bonds are promises to nominal payoffs that can only imperfectly (or not at all) depend on the realization of the state of nature. We also assume sticky wages. So, as in textbook models, monetary and exchange rate policy matters: in the presence of external shocks, flexible exchange rates stabilize labor supply and output at the expense of making exchange rates more volatile. But, as emphasized in the more recent literature, unexpected changes in exchange rates also affect wealth and exacerbate the volatility of domestic consumption if domestic residents are long in one currency and short in the other. Therefore, the optimal choice of exchange rate policy by a benevolent central bank depends on the existence and extent of currency mismatches. But in turn these are determined by the optimizing decisions of domestic borrowers and, hence, by their expectations about exchange rate policy. The equilibrium outcome of this interaction is an exchange rate regime and a market allocation such that the market allocation is a competitive equilibrium given the exchange rate regime, and the central bank cannot increase social welfare by deviating to a different exchange regime. We assume that the central bank chooses the exchange rate regime (whether to fix the nominal exchange rate or to let it float and fix the domestic price level instead) after debts and wage contracts have been written. Then market expectations about exchange rate policy play a crucial role in shaping equilibria. In the main version of our model, bonds are assumed to be non-contingent promises to either home or foreign currency. In that setting, there is always an equilibrium with floating exchange rates. So, if agents expect that the central bank will float, they arrange their wage and debt contracts accordingly, given which the central bank indeed finds it optimal to float. But in some cases, there is also an equilibrium with fixed exchange rates: if agents expect fixed rates, they may choose wages and portfolios that make it optimal for the central bank to fix ex post. That is, one can have multiple equilibrium policy regimes. The intuition underlying equilibria with fixed exchange rates is particularly illuminating. If agents expect fixed exchange rates, home and foreign currency debts become perfect substitutes. This may result, in particular, in an asset–liability position that is very long in one currency and short in the other. But then an unanticipated switch from fixed to flexible rates raises the volatility of financial wealth and consumption. This effect can, if the currency mismatch in assets and liabilities is large enough, deter the central bank from disappointing expectations of a currency peg, which then become self-fulfilling. The equilibrium with fixed exchange rates, therefore, resembles “fear of floating”. As emphasized by Calvo and Reinhart (2002), such a fear may be associated with dollarized liabilities. But there are two significant differences between our analysis and previous discussions. First, in our model liability dollarization may not only give rise to fear of floating, but itself may also emerge because of the rational anticipation of that fear. Second, in our model it is the existence of a currency mismatch in assets and liabilities (rather than liability dollarization per se) that generates fear of floating. When there are multiple equilibria, they can be Pareto-ranked. We show that, if utility functions are quadratic or display constant relative risk aversion, the equilibrium involving flexible rates yields higher expected welfare. So if the economy is in a situation in which there are two equilibrium policy regimes, and arbitrary expectations cause the fixed rates equilibrium to materialize, then expected welfare will be inefficiently low. Welfare would increase if the central bank could pre-commit to float the currency, regardless of the composition of agents' portfolios. Alternatively, appropriate regulation of the currency composition of debts can eliminate the Pareto inferior equilibrium with fixed exchange rates. In this sense, the model provides a novel justification for recent policy attempts at “de-dollarization”.3 We also study the case in which domestic bonds are indexed to the price of home output. Equilibrium policy regimes turn out to be harder to pin down; still, under some further assumptions, we are able to identify conditions for fixed rates and flexible rates to be equilibrium policy regimes. Again, there is a range of parameters for which both regimes occur in equilibrium; in those cases, a policy of flexible rates again delivers higher welfare than do fixed rates. The closest forerunner to our paper is by Corsetti and Pesenti (2002). They focus on the endogenous emergence of a currency area in a setting in which firms can choose to set prices in either domestic or foreign currency.4 While our model and Corsetti and Pesenti's are rather different, there is a common intuition underlying the analysis of both: prior to the choice of an exchange rate regime, private agents make choices (the currency denomination of debt in our paper, the currency in which prices are fixed in Corsetti and Pesenti's) that determine their implicit claims to revenues denominated in different currencies. But once such claims are in place, they affect the relative benefits of flexible and fixed exchange rates. Accordingly, the analysis and results of Corsetti and Pesenti's model are similar to the results we find for our model, though the contexts are not the same. Our discussion is close in spirit to that in Chamon and Hausmann (2005). In that paper, if domestic firms have large dollar liabilities, unexpected changes in the real exchange rate can drive the firms into costly bankruptcy. The central bank can react to shocks by allowing the interest rate or the exchange rate to move. If domestic firms expect a policy of stable exchange rates they will borrow in dollars, which ex post may cause the monetary authority to validate such expectations for fear of bankrupting the firms. Hence, expectations of a particular policy can be self-confirming. This conclusion is similar to ours, but there are important differences between the two papers. Chamon and Hausmann focus on the decision by the central bank to let the exchange rate depreciate following a shock, while we focus on the choice of an exchange rate regime: fixing or floating. Therefore, the expected volatility of the exchange rate (and of consumption) and the extent of currency mismatches (as opposed to dollarization per se) play a central role in our results, while they play no role in theirs. Finally, Chamon and Hausmann use an ad-hoc model with an ad-hoc policy objective function, while we develop a model with explicit microfoundations in which the objective function of the government is to maximize the expected utility of the representative agent in society. Our policy message here is similar to that in Caballero and Krishnamurty (2004), which analyzes a model in which financial market imperfections lead agents to under-provide insurance against liquidity shocks. In that model floating the exchange rate is powerless to ameliorate shocks once the quantity of insurance has been chosen, but can help ex ante to induce agents to take greater precautions against shocks. Hence, Caballero and Krishnamurty also argue for pre-committing to a float, though for reasons very different from ours. The next section outlines the basic model, and Section 3 presents the basic results. Section 4 extends the analysis to the case in which peso bonds are indexed, while Section 5 concludes. Some technical material is delayed to Appendix A.

We have built a model in which both portfolio composition and monetary policies are determined optimally. A key implication is that, since optimal portfolios depend on policy and vice versa, there may be more than one equilibrium policy regime. For certain parameter values and shock distributions, expectations may be self-validating: if agents expect fixed rates and arrange their portfolios accordingly, the monetary authority will indeed deliver a fixed exchange rate. This suggests that the fear of floating that allegedly obtains in many countries may be an artifact of arbitrary expectations. What the literature on fear of floating fails to take into account is that the same would happen if agents expected a policy of flexible exchange rates: assets and liabilities would be denominated in such a way as to make floating optimal for the authorities. Which equilibrium the economy land on matters. We show that for plausible functional forms (and lognormality of the shock in the case of indexed bonds), flexible exchange rates deliver higher expected social welfare than fixed rates. Therefore, policies that anchor expectations on the flexible rates outcome–or, alternatively, induce agents to hold a portfolio that is compatible with flexible exchange rates–raise social welfare. One limitation of the analysis is that here portfolio composition is endogenous, but only given the exogenous restrictions on the menu of assets. While we have allowed for an asset menu that included more than the usual non-contingent world currency bonds, it may be desirable and useful to derive market incompleteness from more fundamental assumptions on the environment. That remains a substantial task, however, and we can only leave it for future research. A second limitation is that we have imposed strong restrictions on the environment and policy options. These restrictions were justified on the basis of tractability and analytical convenience, but obviously they will have to be relaxed if the model is to be the basis for more realistic policy evaluation.